Asymptotic variance for sequential sampling without replacement with unequal probabilities

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Description/Abstract

We propose a second-order inclusion probability approximation for the Chao plan (1982) to obtain an approximate variance estimator for the Horvitz and Thompson estimator. We will then compare this variance with other approximations provided for the randomized systematic sampling plan (Hartley and Rao 1962), the rejective sampling plan (Hájek 1964) and the Rao-Sampford sampling plan (Rao 1965 and Sampford 1967). Our conclusion will be that these approximations are equivalent if the first-order inclusion probabilities are small and if the sample is large.